
In this paper, we work with Gaussian random variables \(X \sim N(\mu ,\sigma ^2)\) . Direct computations then yield \(_\gamma (X) = -\mu + (\gamma /2) \sigma ^2\) , which is consistent with the computation in [1]}. Setting \(\gamma \rightarrow 0^+\)  (resp. \(\gamma \rightarrow +\infty \) ) yields the risk-neutral (resp. risk-averse) setting, since \(\mu \)  (resp. \(\sigma ^2\) ) dominates in the former (resp. latter) case.
